Convexity theorem for infinite dimensional isoparametric submanifolds.
We write a cohomological resolution of the sheaf of solutions of the differential operator on a manifold and study the cohomology groups and .
We correct an error in the normalizing constant of resonant states.
In this paper we consider a smooth and bounded domain of dimension with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...